Form-factors of the finite quantum XY-chain

Abstract

Explicit factorized formulas for the matrix elements (form-factors) of the spin operators σ^x and σ^y between the eigenvectors of the Hamiltonian of the finite quantum periodic XY-chain in a transverse field were derived. The derivation is based on the relations between three models: the model of quantum XY-chain, Ising model on 2D lattice and N=2 Baxter-Bazhanov-Stroganov τ^{(2)}-model. Due to these relations we transfer the formulas for the form-factors of the latter model recently obtained by the use of separation of variables method to the model of quantum XY-chain. Hopefully, the formulas for the form-factors will help in analysis of multipoint dynamic correlation functions at a finite temperature. As an example, we re-derive the asymptotics of two-point correlation function in the disordered phase without the use of the Toeplitz determinants and the Wiener-Hopf factorization method.

20 pages; details of the derivation are added, comments on different regimes are given

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• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
• Front dynamics in the XY chain after local excitations
• Effective free-fermionic form factors and the XY spin chain
• A thermal form factor series for the longitudinal two-point function of the Heisenberg-Ising chain in the antiferromagnetic massive regime
• The tau_2-model and the chiral Potts model revisited: completeness of Bethe equations from Sklyanin's SOV method
• Entanglement spreading after local fermionic excitations in the XXZ chain
• Noise amplification at spin-glass bottlenecks of quantum annealing: a solvable model
• Form factors in equilibrium and non-equilibrium mixed states of the Ising model
• Form factors of twist fields in the lattice Dirac theory